Nonadditive measure is a generalization of additive probability measure. Sugeno integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. Integral inequalities play important roles in classical probability and measure theory. The classical Berwald integral inequality is one of the famous inequalities. This inequality turns out to have ...

Abstract In this paper we are presenting the refinements of integral inequalities established for convex functions. Consequently, get several fractional different kinds operators.

We modify the definition of the weighted integral mean so that we can compare two such means not only upon the main function but also upon the weight function. As a consequence, some inequalities between means are proved.

In this paper, we consider a very useful and significant class of convex sets and convex functions that is relative convex sets and relative convex functions which was introduced and studied by Noor [20]. Several new inequalities of Hermite-Hadamard type for relative convex functions are established using different approaches. We also introduce relative h-convex functions and is shown that rela...

In this article, an open problem posed in [12] is studied once again, and, following closely theorems and methods from [5], some extensions of several integral inequalities are obtained.

Integral inequalities with maxima of the unknown function are useful in the study of control theory. Known results were given for Gronwall-Bellman type integral inequalities with the maxima in the form of linear dependence on the unknown function with a single delay term. In this paper we consider a general form of nonlinear integral inequalities with the maxima and more than one delay terms. R...

OuIang inequalities and their generalizations have proved to be useful tools in oscillation theory, boundedness theory, stability theory, and other applications of differential and difference equations. A nice introduction to continuous and discrete OuIang inequalities can be found in 1, 2 , and studies in 3–5 give some of their generalizations to multiple integrals and higher-dimensional space...

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

Various singular integral inequalities play an important role in the development of the theory of differential equations, functional differential equations, and integral equations. For example, Henry 1 proposed a linear integral inequality with singular kernel to investigate some qualitative properties for a parabolic differential equation, and Sano and Kunimatsu 2 gave a modified version of He...

Fractional differential equations and fractional integral equations have gained considerable importance and attention due to their applications in many engineering and scientific disciplines. Gronwall-Bellman inequalities are important tools in the study of existence, uniqueness, boundedness, stability and other qualitative properties of solutions of Fractional differential equations and fracti...